An adult female human, from Old English wifmann, literally female person: wif, female, plus mann, which then meant human being of any sex.
Documented
The wifmann record
Documented: Old English had wer for male human and wif for female human, with mann as the generic person. Wifmann, female person, contracted through wimman to woman; wer survives only inside werewolf, man-wolf. The woe-to-man derivation is a modern pun with no existence in any period text.
Assessment: Documented: the OED and Bosworth-Toller's Anglo-Saxon dictionary carry the full paradigm. Werwolf is the fossil witness.
Stories
Woe to man
The folk reading, circulated for centuries in sermons and now in comment threads: woman is woe plus man, the biblical trouble named in the word. It is a moral etymology, a story told to instruct, and it fails on the phonology alone, wifmann never sounded like woe.
Assessment: Stories: the pun is traceable as preaching device, not as derivation. It tells you what the tellers thought, which was the point.
Interesting claims
The generic collapse
The documented drift underneath the pun: mann narrowed from person to male person over centuries, leaving woman and werewolf as fossils of the older system, and mankind as a contested inheritance. The word woman thus records a time when English needed a special word for female human but not for human.
Assessment: Interesting: the shrinking of man is the real story, and it is in every dictionary. The pun sits on top of a genuine fossil.
Sources and further reading
Oxford English Dictionary, woman: Old English wifmann, female person, wif plus mann
Bosworth-Toller Anglo-Saxon Dictionary, wifmann, wer, mann (the three-term paradigm)
Oxford English Dictionary, werewolf: wer as the surviving male-human fossil
Worth asking
If man originally meant human, who shrank the word, and when?